Private Message/Conversations view messed up

I honestly have no idea what happened (or, frankly, even when, exactly it started), but yesterday my client alerted me that he was unable to reply to messages. I see what’s happening, but I can’t figure out how to fix it.

Sending messages is fine, when you’re in the conversation view, the screen locks its position, and a bunch of the CSS seems to go out the window. It LOOKS like there’s some <div> tag somewhere that isn’t closing properly… or that there’s some CSS error, but I can’t seem to figure it out.